A numerical model for calculation of the restitution coefficient of elastic-perfectly plastic and adhesive bodies with rough surfaces

Abstract

A contact mechanics model based on Boundary Element Method (BEM) is used to simulate the contact of rough spheres having elastic-perfectly plastic adhesive behaviour. The model has been verified for smooth surfaces with the classical Hertz contact behaviour in elastic regime, JKR theory in the adhesive regime and Thornton and Ning's analytical solution in the elasto-plastic adhesive regime. In this paper, the effect of yield stress, interface energy and surface roughness on the Coefficient of Restitution (COR) is investigated and reported. The results show that surface roughness dramatically affects the COR and higher roughness values lead to lower CORs in general. In addition, it is found that in the presence of surface roughness, the COR varies based on different maximum indentation depths in 3 different stages; the asperity dominant, bulk elastic dominant and bulk plastic dominant. Interestingly, it was shown that there is a critical indentation depth beyond which the effect of surface roughness will disappear and rough surfaces act like smooth ones. This critical indentation depth is proportional to the Root Mean Square roughness (Rq) value of the surface. Numerical results suggest that the yield stress influences the COR and higher yields stress results in higher COR for both rough and smooth surfaces. Furthermore, the effect of interface energy on the COR for rough surfaces is minimal and only significant at low indentations.